output, _ = reproject_interp(aia_map, out_wcs, out_shape)
outmap_default = sunpy.map.Map((output, out_header))
outmap_default.plot_settings = aia_map.plot_settings

plt.figure()
plt.subplot(projection=outmap_default)
outmap_default.plot()

######################################################################
# You can use the different assumption that the image lies on the
# surface of a spherical screen centered at AIA, with a radius equal
# to the Sun-AIA distance.  The curvature of the spherical screen is
# not obvious in this plot due to the relatively small field of view
# of AIA (compared to, say, a coronagraph).

with Helioprojective.assume_spherical_screen(aia_map.observer_coordinate):
    output, _ = reproject_interp(aia_map, out_wcs, out_shape)
outmap_screen_all = sunpy.map.Map((output, out_header))
outmap_screen_all.plot_settings = aia_map.plot_settings

plt.figure()
plt.subplot(projection=outmap_screen_all)
outmap_screen_all.plot()

######################################################################
# Finally, you can specify that the spherical-screen assumption should
# be used for only off-disk parts of the image, and continue to map
# on-disk parts of the image to the surface of the Sun.

with Helioprojective.assume_spherical_screen(aia_map.observer_coordinate,
                                             only_off_disk=True):